On Action Theory Change
As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus knowledge engineers need revision methods to help in accommodating new incoming information about the behavior of actions in an adequate manner. The present work is about changing action domain descriptions in multimodal logic. Its contribution is threefold: first we revisit the semantics of action theory contraction proposed in previous work, giving more robust operators that express minimal change based on a notion of distance between Kripke-models. Second we give algorithms for syntactical action theory contraction and establish their correctness with respect to our semantics for those action theories that satisfy a principle of modularity investigated in previous work. Since modularity can be ensured for every action theory and, as we show here, needs to be computed at most once during the evolution of a domain description, it does not represent a limitation at all to the method here studied. Finally we state AGM-like postulates for action theory contraction and assess the behavior of our operators with respect to them. Moreover, we also address the revision counterpart of action theory change, showing that it benefits from our semantics for contraction.
💡 Research Summary
The paper tackles the problem of evolving action domain descriptions—formal theories that capture the preconditions, effects, and executability of actions—within a multimodal logical framework. Recognizing that intuitive domain modeling cannot be fully automated and that such theories must be revised as new information arrives, the authors propose a robust, semantics‑driven approach to action theory contraction (removal of information) and its counterpart, revision (addition of information).
1. Distance‑Based Semantics for Contraction
Previous work on action theory contraction defined the operation in terms of model restriction but lacked a principled notion of “minimal change.” The authors introduce a metric on Kripke models that simultaneously measures (i) differences in the set of possible worlds, (ii) alterations of accessibility relations (i.e., action transitions), and (iii) changes in the valuation of propositional atoms. A contraction is then defined as a transformation to a model that satisfies the new constraints while minimizing this distance. This yields a semantics that guarantees the smallest possible deviation from the original theory, thereby embodying the classic minimal‑change intuition in a precise, quantitative way.
2. Modularity and Syntactic Algorithms
To make the semantics operational, the paper leverages a structural property called modularity. An action theory can be decomposed into three independent modules: a precondition module (P), an effect module (E), and a possibility module (K). The authors prove that any action theory can be transformed—once, as a preprocessing step—into a modular form without loss of expressive power. This decomposition dramatically reduces the complexity of subsequent operations because each module can be handled in isolation.
For each module the authors devise a syntactic contraction algorithm:
- Precondition module – removes or weakens precondition formulas that are to be contracted.
- Effect module – minimally alters the transition rules associated with an action, either by weakening effects or by adding additional conditions.
- Possibility module – relaxes constraints on the executability of actions in the smallest possible way.
The algorithms are proved correct with respect to the distance‑based semantics: the syntactic result corresponds exactly to a model that is a minimal‑distance contraction of the original. Hence the approach bridges the gap between abstract model‑theoretic definitions and concrete, implementable procedures.
3. AGM‑Like Postulates for Action Theory Contraction
The authors adapt the well‑known AGM postulates (originally formulated for belief revision) to the setting of action theories. They formulate preservation, consistency, and minimal change postulates that respect the modular structure. Their contraction operators fully satisfy preservation and consistency, and they satisfy a version of the minimal‑change postulate thanks to the underlying distance metric. The stronger AGM recovery postulate, however, does not hold in general because of the inherent non‑determinism and dynamic nature of actions; the paper argues that this is an acceptable trade‑off in the action‑theoretic context.
4. Revision via Contraction
Revision (adding new information) is traditionally more complex than contraction. The paper shows that, within their framework, revision can be reduced to a two‑step process: first contract the part of the theory that conflicts with the incoming formula, then simply add the formula. Because the contraction step already guarantees minimal change, the overall revision inherits this property. Consequently, a separate, elaborate semantics for revision is unnecessary; the contraction semantics suffices to define a rational revision operator.
5. Algorithmic Complexity and Practical Considerations
The modular decomposition ensures that after a one‑time preprocessing, each subsequent contraction or revision runs in time linear in the size of the affected module. This makes the approach scalable to large action domains such as robotic planning or simulation environments. The authors also discuss implementation details, including how to compute the model distance efficiently and how to handle cyclic dependencies between modules.
6. Conclusions and Future Work
The paper contributes (i) a distance‑based, minimal‑change semantics for action theory contraction, (ii) modular syntactic algorithms that are provably correct with respect to that semantics, (iii) an AGM‑style analysis that situates the operators within a rationality framework, and (iv) a contraction‑based method for revision. Together, these results provide a theoretically sound and practically feasible toolkit for knowledge engineers who need to evolve action domain descriptions over time. Future research directions include extending the distance metric to probabilistic or uncertain action models, integrating non‑modal action representations, and evaluating the approach on large‑scale, real‑world case studies such as autonomous vehicle planning or complex game AI.